Line Shape in the Mirage Experiment

Using a many-body theory, we calculate the change in differential conductance ∆dI/dV after adding an impurity either on a clean surface or inside an elliptic quantum corral. Using the same set of parameteres for both cases, the qualitative features of the voltage dependence of ∆dI/dV observed in recent experiments, are reproduced. Introduction In recent experiments a Co atom (acting as a magnetic impurity) was placed at one focus of an elliptic corral, and a depression in the differential conductance dI/dV as a function of voltage (a signature of the Kondo effect) was observed not only at this focus, but also at the other one [1]. The space dependence of ∆dI/dV (dI/dV after substracting the corresponding result for the empty corral) reflects mainly the density of the eigenstate of two-dimensional free electrons confined in the corral which lies at the Fermi energy. This space dependence has been reproduced by several theories. The voltage dependence is more subtle and requires in principle a many-body calculation of the Kondo resonance. However, most theories treat the interactions in a phenomenological way. Many-body effects were included either by perturbation theory [2] or by numerical diagonalization in a restricted subspace [3]. Unfortunately, since the separation of the relevant eigenstates of the corral (those with a sizeable hybridization with the impurity) is larger than the Kondo temperature [2, 4], these numerical results cannot reproduce the observed line shape. Here we extend our previous approach [2] to the clean surface and take into account the direct tunneling between the tip and the impurity [5], in order to compare the line shape of ∆dI/dV for an impurity inside the corral or on a clean surface.